// MODEL NUMBER: 0295
// MODEL NAME: Circ.Windkessel3
// SHORT DESCRIPTION: Three-element windkessel model
// with a connecting inductor in parallel (W4P), in series (W4S), and with a
// low-resistance Rc, in series with a viscoelastic windkessel (IVW).
import nsrunit;
unit conversion on;
math Circ.Windkessel3 {
realDomain t sec; t.min=0; t.max=0.35; t.delta=0.01;
//PARAMETERS:
real
Rp = 92.2*10^3 dyn*sec*cm^(-5), // Total peripheral resistance
Rc = 3.52*10^3 dyn*sec*cm^(-5), // Aortic characteristic resistance
C = 16.1*10^(-6) cm^5/dyn; // Total systemic arterial compliance
real P0 = 67 mmHg; // initial pressure value
//VARIABLES
real x(t) dyn/cm^2; // The pressure to the head of compliance (C)
real p(t) dyn/cm^2; // Pulsatile ascending aortic pressure
real Pw3(t) mmHg; // Pulsatile ascending aortic pressure in unit of mmHg
extern real q(t) cm^3/sec; // Pulsatile ascending aortic pressure
when (t=t.min) {x = P0-Rc*q(0);}
//Equations:
x:t = -x/(Rp*C)+q/C;
p = x + Rc*q;
Pw3=p;
}
/*
FIGURE: W3
Rc
o---------- /\/\/\/\/\ -----------------
| |
| |
| >
----- >
C ----- > Rp
| >
| |
| |
o---------------------------------------
DETAILED DESCRIPTION:
Three-element windkessel model is a lumped-parameter model of systemic circulation and has
succinct representation of arterial properties such as total periphera resistance (Rp),
Total arterial compliance (C), and aortic characteristic impedance (Rc).
W4P is an alternative four-element windkessel formulation, derived from the three-element
windkessel by connecting an inductance L in parallel with a low-resistance term, Rc, which
is given the meaning of aortic characteristic impedance.
W4S is an alternative four-element windkessel formulation, derived from the three-element
windkessel by connecting an dinductance L in series with a low-resistance term, Rc, which
is given the meaning of aortic characteristic impedance.
IVW is an alternative four-element windkessel formulation, derived from the three-element
windkessel by connecting an inductance L in series with a viscoelastic windkessel, where
a Voigt cell (a resistance, Rd, in series with compliance, C) accounts for viscoelastic
properties of vessel wall motion.
KEY WORDS:
aortic characteriastic resistance, viscoelastic windkessel, electrical analogue,
pulsatile ascending aortic flow, systemic arterial compliance, connecting an inductance, multi-models
REFERENCES:
- Burattini R, Di salvia PO: "Development of systemic arterial mechanical
properties from infancy to adulthood interpreted by four-element windkessel models",
J Appl Physiol 103:66-79, 2007
REVISION HISTORY:
Original Author : Feng Gao Date: 02/15/2010
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2010 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Academic use is unrestricted. Software may be copied so long as this copyright notice is included.
This software was developed with support from NIH grant HL073598.
Please cite this grant in any publication for which this software is used and send an email
with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
*/